Download Solving Using Quadratic Formula

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Section I: Solving Using Quadratic Formula
Quadratic Formula:
Assuming in standard form 0  ax 2  bx  c :
b  b 2  4ac
2a
Example 1: Solve 3x 2  5x  2 using the quadratic formula.
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7x² + 2x – 2 = 0
-2x² + 8x + 5 = 0
Practice. Solve 3x 2  x  4 using the quadratic formula.
Practice. Solve 2x 2  6x  7 using the quadratic formula.
Practice. Solve 2x 2  4x  3 using the quadratic formula.
Section II: Discriminant
The discriminant of a quadratic equation in the form 0  ax 2  bx  c is:
b2  4ac
Discriminant
Positive Square
Number
Positive non- square
number
Zero
Roots
Negative
Use the discriminant to classify the roots
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x  6x  8  0
x² + 8x + 5 = 0
x² - 6x – 1 = 0
x 2  6x  9  0
x 2  6x  10  0
2
Section 3: COMPLETING THE SQUARE
Using Complete the Square to Solve a Quadratic Equation
Example: Solve 2 x 2  24 x  10  0 .
1. Practice. Solve x 2  4x  4  0
2. Practice: Solve 3x 2  24 x  108  0
3. Practice: Solve 2 x 2  12 x  68
Section 4: Radical Expressions
Example 1: Simplify
Example 2: Simplify
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4. Express
in simplest radical form.
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5.
Factoring Review
Concepts:
1) Before factoring, always look for a GCF
2) Difference of Squares: a2 – b2. This is one of the most important factoring patterns. Memorize
it!
 a2 – b2 = (a – b)(a + b).
3) Factoring by Grouping: Factoring ax2 + bx + c = 0 when a > 1.
 Make a t-table: find two numbers whose sum is b and product is ac.
 Break the middle term into two parts based on those factors.
 Factor by grouping – see notes/example.
Section 5: Factoring by grouping:
2) 30 x  33x  18
2
Your turn (on looseleaf please)!!!
a) Factor 6 x  19 x  15 x
3
2
b) Factor 10 x  26 x  12 x
3
2
c) Factor 28 x  10 x  2 x
3
2
d) Factor: 6 x3  3x 2  45
Section 6: Difference of squares
1) Factor x  25
2
2) Factor 64  9x
2
Your turn:
a. t 2  100
b. 49  a 2
c. 9x 2  25y 2
d. 8x 2  32